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mos1635

6 years ago

maybe taht can help
(translation of a paper i found...)

mos1635

6 years ago

Until the late 19th century saw many attempts to explain theoretically the experimental curves of the spectral distribution of blackbody afetikis capacity of the body. However, they failed either because the physicists started from the wrong theoretical basis or because none of them was ready to do the "aponenoimeno representations" of Planck. Let us see the path followed by the physicists at the time.
The black body radiation
As a black body we consider an object that absorbs all incident radiation falling on it. We can assume that a small hole in the wall cavity of a behaves approximately as a black body, because any radiation entering from outside the hole will be absorbed almost completely from the cavity due to multiple reflections inside it.
Conversely if the cavity is at a high temperature, then the energy from the interior cavity radiated to the environment, called blackbody radiation. This energy depends only on the temperature of the walls of the cavity, and does not depend on the type of radiation.
The thermal radiation
All objects at any temperature above zero scale Kelvin, emit electromagnetic radiation, which has as its cause because the temperature is called thermal radiation. The characteristics depend both on the body temperature and the properties of the body. When body temperature is low (300 Kelvin), the wavelengths of radiation that are invisible in the infrared region, so it is not observable. But when the temperature increased, the length L of the thermal radiation shifted towards the visible region. First shown in red and slowly, with increasing temperature, and the other colors. At the end of the body appears white, as shown in the incandescent tungsten filament in a lightbulb.
The radiation from the black body emitted in the form of electromagnetic waves. There are all the frequencies with a different intensity each. With a spectroscope we examine the distribution of the emitted power versus frequency at a given temperature.
The following curves are made exactly this method.
The classical theory trying to explain this phenomenon, consider that the thermal radiation due to thermal oscillations of charged particles which oscillate to the surface of the body and emit electromagnetic radiation, according to the theory of Maxwell. The particles have a continuous distribution of accelerations, and thus explain the continuous spectrum of radiation.
But the classical theory is not sufficient to explain these experimental curves of the emission of thermal radiation from a black body.
Explanation of curves
Many physicists have tried to give explanations for the form of curves. It turned so that the radiation emitted from the cavity is independent of the shape and size of the cavity, they are also independent of the material of the walls, and depends only on the temperature of the cavity. This observation was first done in 1792 by Wedgewood, a porcelain manufacturer, noticed that all bodies rubescent when they arrived at the same temperature. Later, however, the Kirchhoff, in 1859, and scientifically formulated this proposal.
BoltzmannMaxwellTo 1879 the Austrian physicist Stefan experimentally in 1884 by the Boltzmann theory, combining Maxwell's electrodynamics with the heat, took the law
the Stefan - Boltzmann u = F4,
where u is the body's ability afetiki (the strength of electromagnetic radiation emitted per unit area of ​​the body u = P / S).
This relationship tells us that at any temperature T and if there is a body will emit radiation in some spectral range. Even the temperature of 273 K, emit some radiation. Of course every body not only absorbs and emits radiation. So if the temperature T is greater than the temperature of the environment then your body eventually emits radiation.
WienTo physicist 1893 Wien, combining theory with thermodynamic Maxwell managed to show that u afetiki ability of the body was the product of the cube of the frequency for a function of the ratio of frequency to the temperature.
The ability afetiki u resulting from the completion of the following relation for all wavelengths.
RELATIONSHIP Wien
where rl is the spectral distribution function of afetikis capacity and entry for the volume that gives us a spectrometer for each wavelength L. That is, rl is an experimental scale.
The type of Wien plays an important role.
1. Leads to defining the function of two variables F, f T and F to determine the only one variable, the ratio f / T as true c = lf
2. Supports the experimental data were already known.
If the complete spectral distribution function of rl, the relationship of Wien, across the range of frequencies as we mentioned, the ability afetiki u:
O replacing the quotient finally arrive at
LAW of STEFAN - BOLTZMANN
Also the type of Wien, mentioned above, we can find the wavelength lmax where we find the maximum (peak), the function of the spectral distribution of afetikis capacity.
POSITION OF LAW WIEN
with constant C = 2,90 * 10-3 mK.
As shown in the above curves of the spectral distribution of capacity afetikis rl a black hole depending on the wavelength (which have come out experimentally) with increasing temperature, the maximum capacity of afetikis shifted to shorter wavelengths.
If a curve of the spectral distribution of radiation of a black hole we know the wavelength of maximum distribution at a given temperature, we can estimate any other temperature the length of which corresponds to lmax.
The function rl has no limit to the long wavelengths, while the threshold is lor. The price lor the spectral distribution of rl afetikis capacity zero. This value depends only on the temperature of the black body.
Distribution of molecular velocities in Maxwell
Shortly before dawn the 20th century, physicists Boltzmann, Maxwell, Gibbs and others had established the Statistical Mechanics, which described a statistical basis the thermal properties of bodies. The kinetic theory accept that to mathematically describe the kinetic energy of a large number of molecules in a gas, it is necessary to introduce the statistical method. The average speed and speed of the active molecules have greater value than the knowledge of all the speeds of molecules in a given time. We can watch the tiny macroscopic properties of gases.
A graph showing the relationship between the number N of molecules of gas, and the speed v of the molecules are broken down by Maxwell. Correspond to different temperatures and different curves. The curves are the calculated first by Maxwell and therefore bear the name.
One of the basic laws of statistical mechanics, is the equipartition theorem, which follows from Newton's laws. According to this theorem, for a large number of molecules, each with m degrees of freedom, the average energy per degree of freedom of each molecule is equal to (1/2) kT.
In the above plot, which concerns the Maxwell distribution in nitrogen, we observe a remarkable resemblance to the curves of the thermal radiation of black body.
The ultraviolet catastrophe in the region or the discrepancy in the short wavelengths
JeansVlepontas the Rayleigh Jeans and the similarity of the curves in the distributions by Maxwell and the spectral distribution function of rl, encouraged to apply the thermal radiation of the equipartition principle, which proved so successful in the distribution of speeds. in order to calculate the spectral distribution function of afetikis capacity.
They hypothesized that radiation due to a number of oscillators that make up the black body. Also assumed that energy is equally distributed between all possible frequencies of the oscillators doniseos a black body. The combination of the relation E = kT, which gives us the average energy per oscillator (because each oscillator has two degrees of freedom) and a calculation made for the number of oscillators per unit volume, gives the following relations for the spectral distribution function afetikis capacity:
as demonstrated by the RAYLEIGH - JEANS
This attempt, however, led to disastrous results. Why is there a huge difference between the molecules of gas and thermal radiation consists of electromagnetic vibrations.
For long wavelengths (near infrared) tend to match the experimental curve and the curve of the Law of RAYLEIGH - JEANS. But for short wavelengths (in the UV) is complete disagreement. This discrepancy is called "the ultraviolet catastrophe."
The "disaster" occurred due to the use of the theorem of equal distribution of energy.
At short wavelengths that fails completely the effort of RAYLEIGH - JEANS, but confirmed one other guy, the relationship proposed by Wien.
Wien's relationship to the spectral density function of the cavity
The Wien in 1896 resulted in the following imiempeiriki compared to the spectral density function of capacity afetikis:
which is correct for small wavelengths.
So for the same phenomenon, there are two relationships. This is one of the 1896 WIEN, a good approximation for short wavelengths and the other of RAYLEIGH and JEANS, leading to the use of classical physics in the UV damage and complete failure of classical physics to explain the spectral distribution of afetikis ability of the black body.
The Quantum Theory of Max Planck
The resounding failure of classical physics to explain the black body radiation led to a Max Planck, according to him, "aponenoimeno demarche"
First to admit the statistical nature of the laws of thermodynamics, and secondly to admit that the oscillation energy of people not taking continuous values ​​but discrete.
In classical physics the energy of the oscillator E = (1/2) DX2 can take any value, in quantum theory, however, the energy E of the oscillator can take integer values ​​of quantity hf where h is a constant called Planck.
Difference in Classical and Quantum Theory
In classical theory, the radiated energy of a black body can be seen as standing waves produced by or coordinated statements of the cavity, which radiates.
The classical physics also provides infinite total energy density, because it both allows radiation at all frequencies and any other allowed energy level, due to the equal distribution of power between all possible frequencies of vibration. But the electromagnetic field can not have infinite energy.
To the contrary, the Planck energy was allowed a fixed and proportional to the frequency.
So according to the Rayleigh - Jeans in the cavity will be created outside of the base frequency and infinite harmonics with increasing frequency. If true, the equipartition of energy, then the total energy to be finite, and share equally in infinite frequencies, we come to the strange conclusion that it must in every state of vibration corresponds to very low energy.
The proposal by Planck, allows small frequencies have little energy per vibration energy because any vibration is E = hf. But the higher the frequency, while increasing the energy per vibration, but the proposal also provides that Planck reduced the number of oscillators that can hold this energy and limit the contribution of high frequency energy radiated in frequency. The result is that the amount of energy is a moderate, high frequencies, but the number of vibrations is unlimited. Thus the paradox of canceled Jeans, who wanted to have infinite energy oscillators at high frequencies.
Here we see two modes of vibration of radiation at two frequencies n and 2n.
Endorsement Statements radiation per unit frequency and volume for any situation Chance average energy per oscillation condition
Classical Equal always for all situations
The quantum average energy per mode, there are always equal, is the product of quantum energy hn for the probability to suffer this situation (distribution of energy according to the Statistics of Einstein - Bose).
The Planck finally came to the following relationship that describes perfectly the experimental curve for the spectral distribution:
PLANCK LAW
where Eo = hf
For small frequencies, Planck's law leads to the law of the Rayleigh - Jeans
while for large frequencies PF function declines exponentially according to the experimental data and fits to the law of Wien.
This type of Planck marks the deep rift of classical physics, due to the fact that he failed to explain theoretically the experimental curves of the spectral distribution of blackbody afetikis capacity of the body.
The Planck was not too happy with the theory which had to come. He considered it more as a computational trick, rather than as a fundamental principle, which was to cause a fatal breach in the edifice of classical physics.
He described his theory in a question that made him an American physicist Wood, "as an act of desperation who struggled for six years" in which fled because "at all costs had to find a theoretical interpretation, whatever be the cost except of course the violation of two thermodynamic laws. "
But this theorem was an inevitable consequence of statistical mechanics, which is based on classical mechanics.
So the year 1900, or rather December 14, 1900, publishing the work of Planck, was what led to the start of new era.